Question

Arun bought toffees at 6 for a rupee. How many for a rupee he should sell to gain \(20 \%\) ? (a) 3 (b) 4 (c) 5 (d) can't be determined

Short answer

Answer: 5 toffees.

Step-by-step solution

Find the cost price of a single toffee

Arun bought toffees at a rate of 6 toffees for 1 rupee. To find the cost price (CP) of a single toffee, divide the cost (1 rupee) by the number of toffees (6). Thus: Cost Price per toffee = \(\frac{1}{6}\) rupee.

Calculate the selling price for a 20% gain

Now we need to find the selling price (SP) of a toffee that gives Arun a 20% gain. To do this, multiply the cost price of a toffee by 1 plus the desired gain percentage: SP = CP × (1 + gain%) SP = \(\frac{1}{6}\) × (1 + 0.20) SP = \(\frac{1}{6}\) × (1.20) SP = \(\frac{1.20}{6}\) = \(\frac{1}{5}\) rupee The selling price for a 20% gain is \(\frac{1}{5}\) rupee per toffee.

Determine the number of toffees for a rupee to achieve the desired gain

To find out how many toffees Arun should sell for a rupee to achieve the desired gain, we need to determine how many \(\frac{1}{5}\) rupees are there in 1 rupee: Number of toffees needed for a rupee = \(\frac{1}{(\frac{1}{5})}\) Number of toffees needed for a rupee = \(1 × \frac{5}{1}\) Number of toffees needed for a rupee = 5 So, to gain 20% profit, Arun should sell 5 toffees for a rupee. The correct answer is (c) 5.

Key concepts

Cost Price Calculation

Understanding the cost price calculation is essential for anyone interested in business transactions. The cost price, often abbreviated as CP, is the total expenditure incurred by a seller to acquire a product or service. This includes the purchase price, along with any additional costs required to bring the item to a salable condition and location. In the case of Arun who bought toffees, the cost price calculation is simple yet important.

To calculate the cost price per item when a bulk purchase is made, you need to divide the total amount spent by the number of items bought. For Arun, this was calculated as follows:
Cost Price per toffee = Total cost / Number of toffees
In this exercise, Arun bought 6 toffees for 1 rupee, so the cost price per toffee is \( \frac{1}{6} \) rupee.
This calculation forms the basis for further profit analysis and selling price determination.

Selling Price Determination

The selling price (SP) is the amount a customer pays for a product. To establish a selling price that ensures a profit, we start by determining the cost price. Then, we add the desired profit margin. Knowing how to calculate the selling price is crucial for a successful business strategy.

The formula to calculate the selling price for a desired gain is as follows:
Selling Price = Cost Price × (1 + Gain Percentage)
For example, to achieve a 20% profit, Arun would set the selling price of the toffees using this formula:
Selling Price = \( \frac{1}{6} \) × (1 + 0.20) = \( \frac{1}{5} \) rupee per toffee.
It's important to choose a selling price that covers costs and profit without being unattractive to customers.

Percentage Profit

Percentage profit is a measurement of the profitability of a transaction. It describes the profit made as a percentage of the cost price. The formula to find the percentage profit is:
Percentage Profit = ((Selling Price - Cost Price) / Cost Price) × 100%
In business scenarios, including Arun's case, it is vital to determine the percentage profit to set competitive prices and understand the return on investment. By deciding he wanted a 20% profit, Arun used the percentage to calculate his selling price effectively:
Percentage Profit = 20% => 0.20 in decimal
This approach helped Arun to define that he should sell fewer toffees per rupee—setting the number at 5 to attain his profit goal.

Quantitative Aptitude

Quantitative aptitude refers to the ability to handle numerical and mathematical calculations. It often includes problems related to arithmetic, algebra, geometry, and data interpretation. This skill is vital for making effective business decisions, such as those needed for profit calculations and selling strategies.

In the exercise involving Arun and his toffees, quantitative aptitude was necessary to perform operations such as division to find the cost price per toffee, multiplication to determine the selling price with a profit margin, and inverse operations to figure out the number of toffees that could be sold for a rupee to maintain the desired profit percentage.

With strong quantitative aptitude, students and professionals alike can solve such problems with confidence, ensuring precision in profit calculations and business strategies.